ND leads 80-13-1. At one point had won 43 straight times. To me this is just an annual game. USC is an example of an ND rival.
They play annually so they are rivals or teams who play annually? ND fans get excited for other matchups and just hope to leave Navy without injuries.
I see a rival as someone where both schools care. At ND this is not a celebrated game like others, similar to us vs USU.
ND vs Navy even has cool story, yet not a rivalry.